Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design
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Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design

Authors: Li Jie, Zhang Wei

Abstract:

In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126994

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References:


[1] B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: Modelling, Planning, and Control: Springer Publishing Company, Incorporated, 2008.
[2] R. Soltani-Zarrin, and S. Khanmohammadi, "A Novel Approach for Scheduling Rescue Robot Mission Using Decision Analysis", World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering, vol.8, no.2, 2014, pp.387-393.
[3] M. Bernard et al. "Autonomous transportation and deployment with aerial robots for search and rescue missions." Journal of Field Robotics 28.6 (2011), pp. 914-931.
[4] S. Carpin, et al. "High fidelity tools for rescue robotics: results and perspectives." Robot Soccer World Cup. Springer Berlin Heidelberg, 2005.
[5] S. Khanmohammadi, and R. Soltani-Zarrin, "Intelligent Path Planning for Rescue Robot", World Academy of Science, Engineering, and Technology, International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering, vol.5, no.7, 2011, pp. 839-844.
[6] A. Kleiner, and C. Dornhege. "Real‐time localization and elevation mapping within urban search and rescue scenarios." Journal of Field Robotics 24.8‐9 (2007): 723-745.
[7] G. Shilpa, and B. Kuipers. "High performance control for graceful motion of an intelligent wheelchair." Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on. IEEE, 2008.
[8] T. Carlson, and Jose del R. Millan. "Brain-controlled wheelchairs: a robotic architecture." IEEE Robotics and Automation Magazine 20. EPFL-Article-181698 (2013): 65-73.
[9] R. M. DeSantis, "Modeling and path-tracking control of a mobile wheeled robot with a differential drive." Robotica 13.04 (1995): 401-410.
[10] R. Soltani-Zarrin, and S. Jayasuriya, "Constrained directions as a path planning algorithm for mobile robots under slip and actuator limitations," in Proc. 2014 IEEE/RSJ Intelligent Robots and Systems Conf., Chicago, 2014, pp. 2395-2400.
[11] R. Balakrishna, and A. Ghosal. "Modeling of slip for wheeled mobile robots." IEEE Transactions on Robotics and Automation 11.1 (1995), pp. 126-132.
[12] A. Astolfi, “Discontinuous Control of the Brockett Integrator.” European Journal of Control. Vol. 4(1):49-63; 1998.
[13] A. Zeiaee, R. Soltani-Zarrin, S. Jayasuriya, and R. Langari, "A Uniform Control for Tracking and Point Stabilization of Differential-Drive Robots Subject to Hard Input Constraints," in Proc. ASME 2015 Dynamic Systems and Control Conference, Columbus, 2015, pp. V001T04A005.
[14] A. Astolfi, “Exponential Stabilization of a Wheeled Mobile Robot Via Discontinuous Control.” ASME Journal of Dynamic Systems, Measurements, and Control. March, 1999.
[15] C. Samson and K. Ait-Abderrahim, "Feedback control of a nonholonomic wheeled cart in Cartesian space," in Robotics and Automation, 1991. Proceedings., 1991 IEEE International Conference on, 1991, pp. 1136-1141 vol.2.
[16] C. Samson, “Time-varying feedback stabilization of carlike wheeled mobile robots,” International Journal of Robotics Research. Vol. 12:55-64; 1993.
[17] G. Walsh, D. Tilbury, S. Sastry, and J.P. Laumond, “Stabilization of trajectories for systems with nonholonomic constraints,” IEEE Transactions on Automatic Control. Vol. 39(1):216-222; 1994.
[18] A. Tayebi, M. Tadjine, and A. Rachid, “Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot.” Nonlinear Dynamics. Vol. 24:167-181; 2001.
[19] P. Tsiotras, “Invariant Manifold Techniques for Control of Underactuated Mechanical Systems.” Modeling and Control of Mechanical Systems. Imperial College, London, UK; 1997. pp. 277-292.
[20] B. d'Andrea-Novel, G. Campion, and G. Bastin, "Control of nonholonomic wheeled mobile robots by state feedback linearization," Int. J. Rob. Res., vol. 14, 1995, pp. 543-559
[21] A. Zeiaee, R. Soltani-Zarrin, and R. Langari, "Novel Approach for Trajectory Generation and Tracking Control of Differential Drive Robots Subject to Hard Input Constraints," in Proc. 2016 American Control Conference, Boston, 2016, pp. 2098-2103.
[22] B. d'Andrea-Novel, G. Bastin, and G. Campion, "Dynamic feedback linearization of nonholonomic wheeled mobile robots," in Robotics and Automation, 1992. Proceedings., 1992 IEEE International Conference on, 1992, pp. 2527-2532
[23] G. Oriolo, A. De Luca, and M. Vendittelli, "WMR control via dynamic feedback linearization: design, implementation, and experimental validation," Control Systems Technology, IEEE Transactions on, vol. 10, pp. 835-852, 2002.
[24] Brockett, R. W., 1983, “Asymptotic Stability and Feedback Stabilization”, Differential Geometric Control Theory, R.W. Brocket, R. S. Milman, H. J. Sussman, eds., Birkhauser, Boston, pp. 181-191.
[25] A. De Luca and M. D. Di Benedetto, "Control of nonholonomic systems via dynamic compensation," Kybernetika, vol. 29, pp. 593-608, 1993.
[26] J. Zhong-Ping and H. Nijmeijer, "A recursive technique for tracking control of nonholonomic systems in chained form," Automatic Control, IEEE Transactions on, vol. 44, pp. 265-279, 1999.
[27] W. E. Dixon, D. M. Dawson, F. Zhang, and E. Zergeroglu, "Global exponential tracking control of a mobile robot system via a PE condition," Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 30, pp. 129-142, 2000.
[28] R. Soltani-Zarrin, A. Zeiaee, and S. Jayasuriya, "Pointwise Angle Minimization: A Method for Guiding Wheeled Robots Based on Constrained Directions," in Proc. ASME 2014 Dynamic Systems and Control Conference, San Antonio, 2014, pp. V003T48A004.
[29] Khalil, Hassan K., and J. W. Grizzle. Nonlinear systems. Vol. 3. New Jersey: Prentice hall, 1996.
[30] Liao, Tianjun, et al. "Ant Colony Optimization for Mixed-Variable Optimization Problems." Evolutionary Computation, IEEE Transactions on 18.4 (2014), pp. 503-518.
[31] H. Kharrati, S. Khanmohammadi, A. Zeiaee, A. Navarbaf, and G. Alizadeh, “Design of Optimized Fuzzy Model-Based Controller for Nonlinear Systems Using Hybrid Intelligent Strategies”, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 226, no. 9, Oct. 2012, pp. 1152-1165.
[32] A. Zeiaee, H. Kharrati, and S. Khanmohammadi. "Optimized Fuzzy PDC Controller for Nonlinear Systems with TS Model Mismatch.", in Proc. of IEEE International Conference on Advanced Mechatronic Systems, Zhengzhou, 2011, pp. 61-66.
[33] Zhang, Li-Biao, et al. "Application of Particle Swarm Optimization for Solving Optimization Problems." Journal of Jilin University (Information Science Edition) 23.4 (2005), pp. 385-389.